This paper investigates the recursive adaptive algorithms for rapidly detecting various stochastic trends in signals by modeling them as the autoregressive integrated(ARI) process. In order to determine the degree of differencing which represents the changing rate of nonstationary trend components, we derive a new criterion on a basis of the concept of the AIC. The generalized gradient(GG) algorithm and the normalized least squares lattice(NLSL) filter are utilized to identify coefficient parameters in the ARI model in an on-line manner. The effectiveness of the algorithms is examined through numerical simulation using actual data.